The family-run Sumal newsagents on Newington Road first received a visit from police towards the end of last year after a local mother complained that her child had succeeded in buying alcohol at the shop.
Despite the visit, police twice spotted youths leaving the with carrier bags full of cider and Buckfast wine.
The city council's licensing committee has now suspended the shop's right to sell alcohol for six months.
Inspector Gordon Hunter, representing the chief constable, told councillors that the incidents showed licensee Baldish Singh was not a fit and proper person to hold a licence.
It emerged that police received a tip-off last year that the shop was "freely" selling alcohol to underage customers. Officers visited the premises and warned staff not to do it again.
But in December police spotted two youngsters hanging about the shop front, before entering then leaving with a carrier bag full of alcohol, which police then seized.
In March plain-clothes officers noticed a similar scenario when a group of youths left the shop with a mix of lager, cider and Buckfast. When police caught up with the group member who bought the alcohol, he said he hadn't been asked for identification.
Inspector Hunter said: "If any kind of system did exist (for checking customers' ages) it was ineffective.
"I don't think it is unreasonable to expect a shop to ask a customer how old they are.
"We don't consider her (Mrs Singh) to be a fit and proper person and ask the board to consider suspending the licence."
Mrs Singh runs the shop, which she acquired 18 months ago, along with her husband and son.
She has been in the industry without a black mark for 30 years, her lawyer said, and she was not in the shop when any of the incidents took place.
Her lawyer Alistair MacDonald added: "Those who bought alcohol were 17 and 16, it's not like it was 13 and 14-year-olds going into the shop.
"These two incidents have occurred and the staff genuinely believed they were 18. They have to now show that this won't happen again, they introduced an over-21s policy and a CCTV camera facing the customer. They also passed a recent test purchasing scheme by police and Mrs Singh has been on a training course."
Despite the pleas, the committee decided to issue the suspension.
Licensing convener Councillor Marjorie Thomas said: "The board take these incidents very seriously. If it had been 13 and 14-year-olds (buying the alcohol) the length of suspension might have been longer. This is such a big issue."
Both Mr and Mrs Singh declined to comment when approached by the Evening News.